Search Results

You are looking at 1 - 9 of 9 items for

  • Author or Editor: Zavis̆a I. Janjić x
  • Refine by Access: All Content x
Clear All Modify Search
Zaviša I. Janjić

Abstract

A procedure leading to a stable space-centered, leapfrog time-differencing scheme, capable of preventing the false two-grid-interval noise that arises when two large-scale solutions are separated an different elementary subgrids, is presented.

Full access
Zavisa I. Janjić

Abstract

A common problem with nonlinear advection schemes is the false accumulation of energy at the smallest resolvable scales. To keep this process under control, following Arakawa (1966), a number of energy and enstrophy conserving schemes for staggered and semi-staggered grids have been designed. In this paper, it is demonstrated that, in contrast to the staggered grid, the conservation of energy and enstrophy on the semi-staggered gods does not guarantee that the erroneous transport of energy from large to small scales will be effectively restricted.

Using a new approach to the application of the Arakawa Jacobian, a scheme for a semi-staggered grid which exactly reflects the Arakawa theory for nondivergent flow is obtained for the first time. This is achieved by conservation of energy and enstrophy as defined on the staggered grid. These two quantities are of higher accuracy and cannot be calculated directly from the dependent variables on the semi-staggered grid. It is further demonstrated that the amount of energy which can be transported toward smaller scales is more restricted than for any other scheme of this type on both staggered and semi-staggered grid.

Experiments performed with the proposed scheme and a scheme which conserves energy and enstrophy as defined on the semi-staggered grid reveal visible differences in long-term integrations which are in agreement with the theory and demonstrate the advantages of the new scheme.

Full access
Zavis̆a I. Janjić

Abstract

The pressure gradient force error of the spectral technique used in combination with the σ vertical coordinate was examined in an idealized case of an atmosphere at rest and in hydrostatic equilibrium. Small-scale (one-point and three-point) mountains were used in the tests. With such definitions of topography, difficulties could be expected with the spectral method due to slow convergence of the Fourier series. For reference, the finite-difference pressure gradient force errors were also computed. In the examples considered, it. was found that the errors of the spectral method can be large. In the rms sense, the spectral pressure gradient force errors were larger than those of the finite-difference method.

Full access
Full access
Zaviša I. Janjić

Abstract

A comprehensive physical package has been developed for a regional eta coordinate model with the steplike mountain representation. This paper describes the basic problems, concepts and numerical techniques developed, and reviews primarily those aspects of the performance of the model which reflect the effects of the parameterized physical processes.

The Level 2.5 turbulence closure model in the Mellor-Yamada hierarchy was chosen to represent the turbulence above the surface layer. A severe instability encountered in the early experiments in the turbulent kinetic energy (TKF) equation was found to be of a numerical origin. The instability was removed by a suitably designed time-differencing scheme. As implemented in the eta-coordinate model, the Level 2.5 turbulence closure model is computationally remarkably inexpensive. An unconditionally stable, trivially implicit, time-differencing scheme is proposed for the vertical diffusion.

The Mellor-Yamada Level 2 turbulence closure scheme is used for the surface layer. For additional flexibility, a shallow logarithmic, dynamical turbulence layer, is introduced at the bottom of the Level 2 surface layer. A rather conventional formulation has been chosen for the ground surface processes and surface hydrology.

The nonlinear fourth order lateral diffusion scheme was implemented in the model. The diffusion coefficient depends on deformation and TKE. The ratio of the horizontal turbulent coefficients for momentum and heat was estimated. The divergence damping is used as another mechanism for maintaining the smoothness of prognostic fields and/or accelerating the geostrophic adjustment.

The Betts and Miller approach has been adopted for deep and shallow cumulus convection. The formulation of the large-scale condensation is rather conventional, and includes the evaporation of precipitating water in the unsaturated layers below the condensation level.

A review of the available results of numerical experiments suggests that the eta model is competitive with other sophisticated models using similar resolutions, and requiring similar computational effort. Thus, it is believed that the viability of the eta coordinate step-mountain approach in grid point models has been finally demonstrated.

Full access
Zaviša I. Janjić

Abstract

The step-mountain eta model has shown a surprising skill in forecasting severe storms. Much of the credit for this should be given to the Betts and Miller (hereafter referred to as BM) convection scheme and the Mellor-Yamada (hereafter referred to as MY) planetary boundary layer (PBL) formulation. However, the eta model was occasionally producing heavy spurious precipitation over warm water, as well as widely spread light precipitation over oceans. In addition, the convective forcing, particularly the shallow one, could lead to negative entropy changes.

As the possible causes of the problems, the convection scheme, the processes at the air-water interface, and the MY level 2 and level 2.5 PBL schemes were reexamined. A major revision of the BM scheme was made, a new marine viscous sublayer scheme was designed, and the MY schemes were retuned.

The deep convective regimes are postulated to be characterized by a parameter called “cloud efficiency.” The relaxation time is extended for low cloud efficiencies and vice versa. It is also postulated that there is a range of reference equilibrium states. The specific reference state is chosen depending on the cloud efficiency. The treatment of the shallow cloud tops was modified, and the shallow reference humidity profiles are specified requiring that the entropy change be nonnegative.

Over the oceans there are two layers: (a) a viscous sublayer with the vertical transports determined by the molecular diffusion, and (b) a layer above it with the vertical transports determined by the turbulence. The viscous sublayer operates in different regimes depending on the roughness Reynolds number.

The MY level 2.5 turbulent kinetic energy (TKE) is initialized from above in the PBL, so that excessive TKE is dissipated at most places during the PBL spinup. The method for calculating the MY level 2.5 master length scale was rectified.

To demonstrate the effects of the new schemes for the deep convection and the viscous sublayer, tests were made using two summer cases: one with heavy spurious precipitation, and another with a successful 36-h forecast of a tropical storm. The new schemes had dramatic positive impacts on the case with the spurious precipitation. The results were also favorable in the tropical storm case.

The developments presented here were incorporated into the eta model in 1990. The details of further research will be reported elsewhere. The eta model became operational at the National Meteorological Center, Washington, D.C., in June 1993.

Full access
Millan Dragosavac and Zavisa I. Janjic

Abstract

The effect of the grid choice on the stationary solutions of the linearized shallow water equations in the presence of topography is examined.

The time-averaged numerical solutions on the C grid reported by Arakawa and Lamb as well as the B-grid solutions of Dragosavac et al. may be considered to belong to this class. Namely, due to the time-averaging, the transient motions are, to a large extent, filtered out, leaving behind the predominantly stationary part. The absolute values of the ratios of the amplitudes of the finite-difference and exact solutions have been chosen as the measure of the error introduced by the finite-differencing.

The results obtained suggest that with reasonable resolution the horizontal space arrangement of dependent variables may affect the finite-difference solutions on the synoptic scales.

Full access
Fedor Mesinger, Zaviša I. Janjić, Slobodan Ničković, Dušanka Gavrilov, and Dennis G. Deaven

Abstract

The problem of the pressure gradient force error in the case of the terrain-following (sigma) coordinate does not appear to have a solution. The problem is not one of truncation error in the calculation of space derivatives involved. Thus, with temperature profiles resulting in large errors, an increase in vertical resolution may not reduce and is even likely to increase the error. Therefore, an approach abandoning the sigma system has been proposed. It involves the use of “step” mountains with coordinate surfaces prescribed to remain at fixed elevations at places where they touch (and define) or intersect the ground surface. Thus, the coordinate surfaces are quasi-horizontal, and the sigma system problem is not present. At the same time, the simplicity of the sigma system is maintained.

In this paper, design of the model (“silhouette” averaged) mountains, properties of the wall boundary condition, and the scheme for calculation of the potential to kinetic energy conversion are presented. For an advection scheme achieving a strict control of the nonlinear energy cascade on the semistaggered grid, it is demonstrated that a straightforward no-slip wall boundary condition maintains conservation properties of the scheme with no vertical walls, which are important from the point of view of the control of this energy cascade from large to small scales. However, with that simple boundary condition considered, momentum is not conserved. The scheme conserving energy in conversion between the potential and kinetic energy, given earlier for the one-dimensional case, is extended to two dimensions.

Results of real data experiments are described, testing the performance of the resulting “Step-mountain” model. An attractive feature of a step-mountain (“eta”) model is that it can easily be run as a sigma system model, the only difference being the definition of ground surface grid point values of the vertical coordinate. This permits a comparison of the sigma and the eta formulations. Two experiments of this kind have been made, with a model version including realistic steep mountains (steps at 290, 1112 and 2433 m). They have both revealed a substantial amount of noise resulting from the sigma, as compared to the eta, formulation. One of these experiments, especially with the step mountains, gave a rather successful simulation of the perhaps difficult “historic” Buzzi–Tibaldi case of Genoa lee cyclogenesis. A parallel experiment showed that, starting with the same initial data, one obtains no cyclogenesis without mountains. Still, the mountains experiment did simulate the accompanying midtropospheric cutoff, a phenomenon that apparently has not been reproduced in previous simulations of mountain-induced Genoa lee cyclogeneses.

For a North American limited area region, experimental step-mountain simulations were performed for a case of March 1984, involving development of a secondary storm southeast of the Appalachians. Neither the then operational U.S. National Meteorological Center's Limited Area Forecast Model (LFM) nor the recently introduced Nested Grid Model (NGM) were successful in simulating the redevelopment. On the other hand, the step-mountain model, with a space resolution set up to mimic that of NGM, successfully simulated the ridging that indicates the redevelopment.

Full access
Alan K. Betts, Fei Chen, Kenneth E. Mitchell, and Zaviša I. Janjić

Abstract

Data from the 1987 summer FIFE experiment for four pairs of days are compared with corresponding 48-h forecasts from two different versions of the Eta Model, both initialized from the NCEP–NCAR (National Centers for Environmental Prediction–National Center for Atmospheric Research) global reanalysis. One used the late 1995 operational Eta Model physics, the second, with a new soil and land surface scheme and revisions to the surface layer and boundary layer schemes, used the physics package that became operational on 31 January 1996. Improvements in the land surface parameterization and its interaction with the atmosphere are one key to improved summer precipitation forecasts. The new soil thermal model is an improvement over the earlier slab soil model, although the new skin temperature generally now has too large a diurnal cycle (whereas the old surface temperature had too small a diurnal cycle) and is more sensitive to net radiation errors. The nighttime temperature minima are often too low, because of a model underestimate of the downwelling radiation, despite improvements in the coupling of the surface and boundary layer at night. The daytime incoming solar radiation has a substantial high bias in both models, because of some coding errors (which have now been corrected), insufficient atmospheric shortwave absorption, and underestimates of cloud.

The authors explore evaporation before and after a midsummer heavy rain event with the two models. The late 1995 operational model uses a soil moisture bucket physics, with a specified annual-mean fixed field soil moisture climatology, so the surface evaporation responds primarily to the atmospheric forcing. While the surface fluxes in the new model show this strong rain event more dramatically, because its soil moisture comes from the global reanalysis rather than climatology, there remain problems with soil moisture initialization. It appears that a fully continuous Eta data assimilation system (which is under development), likely with more than two soil layers and assimilation of observed hourly precipitation, will be needed to get an adequate soil moisture initialization. Evaporation in the new two-layer soil model falls too much from forecast day 1 to day 2, as the first shallow 10-cm layer dries out (as it also does in the 1995 model with the bucket physics). This appears to be related to the specified low vegetation fraction and the bare soil evaporation model. Although the new boundary layer scheme is better coupled to the surface at night, both versions underestimate entrainment at the top of the mixed layer. The improvement in the surface evaporation resulting from using a climatological green vegetation fraction (derived from satellite data) and a revised bare soil evaporation formulation are shown. These changes were incorporated in a model physics revision in February 1997. An encouraging result from one case study, when it rained in the model, shows that the interaction between the surface, boundary layer, and convection schemes during precipitation is satisfactory, although the model underestimates the impact of cloud cover on the incoming solar radiation.

Full access